idk i’m bad at math

[limber basalt]

How do I make it so y= something

[limpid spade]

,w x^2+y^2 = sqrt(x+y)

[quaint karma]

Sending query to Wolfram Alpha, please wait.

[limpid spade]

hmm squaring both sides is no use

[strange flower]

You end up with a quartic equation, which is going to be pretty damn hard to solve

[limpid spade]

Wolfram is going crazy

[strange flower]

!xy

[clear spade]

Please show the original problem, exactly as it was stated to you, with the entire original context. A picture or screenshot is best. If the original problem is not in English, then post it anyway! The additional context might still be helpful. Do your best to provide a translation.

[limpid spade]

And that's just one of two

Actually more LOL

[idle jungle]

it’s pretty hard u have to let x+y = another variable say U, Then let y= U-x, sub in and use numerical methods

y=-x, and 1-x is what GPT says

try at doesn’t work tho i think

[strange flower]

!nogpt

[clear spade]

Please do not trust ChatGPT or similar AI tools for mathematical tasks, as they often generate output which "sounds correct" but has numerous factual or logical errors. Use of these AI tools to answer other people's help questions is strictly against server rules (see #rules).

[ashen osprey]

no its just beautiful

[vital mica]

Square both sides to get it into equivalent form (x^2+y^2)^2 = x + y. Then expand it into y^4 + 2x^2y^2 - y + x^4 - x = 0. Then either use the general quartic formula or a version of it where the cubic terms is zero. You will get something that doesn't look pretty even after simplification. The reason it doesn't look pretty is that the curve isn't symmetric along the x and y axes but along the x+y and x-y axes. To make it prettier we do a change of variables a = x+y, b = x-y and now we can easily solve for b = +-sqrt(2sqrt(a)-a^2)

There is no other way to solve for y than to somehow "solve" this reduced quartic and it will be tedious and look complicated

[thorny trail]

its not a linear function i think it was impossible to find y=?

[vital mica]

No. Being non-linear doesn't make it impossible as long as you are willing to have multiple branches. Like for example you can represent a circle x^2 + y^2 = 1 using the two branches of the square root i.e. y = +- sqrt(1 - x^2). Here you can also represent y using two branches, but that requires solving a quartic equation.

[vital mica]

If you put the original equation into wolfram alpha you get the two branches like this for all x that are possible which join into a single branch at the minimum and maximum of x

Also you might not even require multiple branches in some non-linear cases. As long as you can separate terms with y out and the function in y they form is invertible

Like e^y = x gives you y = log x for positive x.

[limpid spade]

Sorry but my life isn't as linear as you think